### Author Topic: Arithmetic help gratefully accepted!  (Read 5412 times)

#### AllanEaton

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##### Arithmetic help gratefully accepted!
« on: December 22, 2015, 11:56:35 PM »
Greetings all! I'm new to the Forum but have been reading for some months now and benefitting from all the good thinking and goodwill. Now I have a question of my own that has me surprisingly baffled.

I'm a member of a defined benefit pension plan, and am contemplating retiring in the next year (not RE really, as I'll be 57!). The plan gives me a choice:

• Option 1 = start pension payments right away, at \$X a year.
• Option 2 = start pension payments at 60, at about \$X x 1.16 a year.

For some reason I'm having a heck of a time figuring out which of these is the better choice in dollar terms. I can live pretty well on the \$X amount, and I have (more than) the \$3X available to fill in those 3 years if I choose Option 2. But there must be a simple formula I can use to determine which one will deliver more \$ over a given number of years -- or how many years I would have to live to make Option 2 more lucrative overall. No need for the time value of money to figure into it; given current interest rates let's round to zero.

Any algebraically gifted mustachians who can help?

Gratias!

#### JZinCO

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##### Re: Arithmetic help gratefully accepted!
« Reply #1 on: December 23, 2015, 12:16:19 AM »
If you plan on living to 79 or longer, take option 2. 22 years is the breakeven point between each option.
« Last Edit: December 23, 2015, 08:55:44 AM by JZinCO »

#### JZinCO

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##### Re: Arithmetic help gratefully accepted!
« Reply #2 on: December 23, 2015, 12:23:28 AM »
I'll add in that if you plan on investing the money, the arithmetic does change dramatically. For example, if you invested 100% of the funds in either case and earned 3% interest, it would take 33 years for option 2 to be worth more than option 1.

So you know, might be worth doing the math with a consideration of how the money would be managed.

#### Exflyboy

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##### Re: Arithmetic help gratefully accepted!
« Reply #3 on: December 23, 2015, 12:42:12 AM »
Also the compound growth rate is 5.1% (assuming 3 full years between now and future).

If you assume inflation running between 2 and 3%, then by waiting you are beating inflation.. in other words if you wait the three years your spending power will be greater in 3 years than it is today.

So live off your savings for three years if you can is the better deal. Of course the problem is you may never draw your pension if you have enough other savings to tap..:)

#### AllanEaton

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##### Re: Arithmetic help gratefully accepted!
« Reply #4 on: December 23, 2015, 12:49:56 PM »
Thanks for your quick replies, JZ and Exfly; both very helpful. I do still find myself a bit muddled, though. Maybe if I set out an example you can clear up where I'm going wrong.

My assumed life expectancy is 85 years, so I'm looking at drawing the pension for either 28 (Option 1) or 25 (Option 2) years. If I go with Option 1 I get 28 times \$x; with Option 2, 25 times 1.16 or 29 times \$x. So in terms of the pension benefit itself, Option 2 is better.

But if my spending for the first three years will be at least \$x a year, shouldn't I deduct 3x from the Option 2 total, leaving it at just 26 times \$x? Or am I introducing an apple into a comparison of oranges?

Again, I really appreciate your help working this through; my uncharacteristic innumeracy around it is bugging me.

AE

#### JZinCO

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##### Re: Arithmetic help gratefully accepted!
« Reply #5 on: December 23, 2015, 01:21:13 PM »
You're already accounting for those 3 years where you say you draw the pension for either 28 or 25 years.

It will still take 22 years for option 2 to have paid out more than option 1 whether you are spending all or none of it.

#### arebelspy

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##### Re: Arithmetic help gratefully accepted!
« Reply #6 on: December 23, 2015, 01:31:24 PM »
Here's a simple spreadsheet to illustrate JZ's point.

Sheet one (the tabs) has if you just collect and spend it.  You can see at age 78, the cumulative amount collected of option 2 passes option one.  So if you live to be older than 78, option 2 nets you more.

Sheet 1 shows JZ's first and latest post in this thread.

This is a very simplistic way to look at it.  Given that you can collect earlier with option one, and money now is worth more than future money, finding the net present value of each option is more useful.

This is on sheet 2 (second tab of the spreadsheet), which shows JZ's second post in this thread.

You can change the discount rate (cell E1), but basically if you got 3% or higher, option 2 will never beat option one, only at <3% will you see option 2 win.

I'd personally be going for option one, for the bird in the hand of both you potentially dying and for them becoming potentially insolvent or have to cut pensions (both are "get the money while you can" ideas), as well as the fact that the NPV of the money now indicates--to me--the options are close enough that if you're investing any of it, it's worth getting it earlier.  Since you say you have the 3X to cover you for the next few years, you can invest that money (live off the pension and invest that current money, or live off that money and invest the pension money, doesn't make a difference), so option 1 seems better to me, unless you're SUPER risk adverse and have no money invested, just sitting in cash.
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
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#### JZinCO

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##### Re: Arithmetic help gratefully accepted!
« Reply #7 on: December 23, 2015, 01:42:34 PM »
Thanks for setting up those charts.

One last thing to remember is that COLA, if available, compounds. That gives an advantage to option 2.

I'd personally be going for option one, for the bird in the hand of both you potentially dying and for them becoming potentially insolvent or have to cut pensions (both are "get the money while you can" ideas), as well as the fact that the NPV of the money now indicates--to me--the options are close enough that if you're investing any of it, it's worth getting it earlier.  Since you say you have the 3X to cover you for the next few years, you can invest that money (live off the pension and invest that current money, or live off that money and invest the pension money, doesn't make a difference), so option 1 seems better to me, unless you're SUPER risk adverse and have no money invested, just sitting in cash.
I wholeheartedly agree. I said in my first post to take the latter option; I should have written that based on how the question was framed option 2 wins. If it were me I would take option 1 because of the reasons Rebel Spy laid out. I know I would find a way to earn some amount on those dollars and trim the actuarial advantage of option 2.

edit: The question posed is actually one of those times when it may be worth talking to a personal finance professional. As a rebel spy mentioned with net present value, there may actually be a better way to frame the question. My guess is you probably need to be more holistic and include other variables regarding your personal finances. Maybe you have an accountant friend?
« Last Edit: December 23, 2015, 01:48:13 PM by JZinCO »

#### arebelspy

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##### Re: Arithmetic help gratefully accepted!
« Reply #8 on: December 23, 2015, 01:49:48 PM »
Thanks for setting up those charts.

One last thing to remember is that COLA, if available, compounds. That gives an advantage to option 2.

Except that it compounds at the rate of inflation or below, likely, so investing earlier still probably comes out ahead.  But it does add a wrinkle.

Definitely agree with you that it's a complicated question.  It'd be worth sitting down for a few minutes, answering some questions about your various assumptions/projections of the future, and what exactly you'll do with the money, and run scenarios based on that to find which you're more comfortable with.
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### AllanEaton

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##### Re: Arithmetic help gratefully accepted!
« Reply #9 on: December 23, 2015, 01:54:22 PM »
Thank you both so much! This is exactly what I needed, in that you've not only answered my specific questions but pointed out how to refine the analysis. COLA, rate of return and insolvency risk all will figure in my decision-making, thanks to this exchange.

Special hat-tip to Arebelspy for the tables.

Best of the season,

AE

#### arebelspy

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##### Re: Arithmetic help gratefully accepted!
« Reply #10 on: December 23, 2015, 02:15:13 PM »
No problem!

If you want to throw out your thoughts on the various variables, we can probably help refine more and suggest other possibilities, or if you're good to go on your own from here, great.

Welcome to the forums!
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### MDM

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##### Re: Arithmetic help gratefully accepted!
« Reply #11 on: December 23, 2015, 06:57:41 PM »
If you are planning to spend the pension, the NPV calculation discussed above is probably best.

If you are planning to invest the pension, then you want the Future Value (FV) calculation instead of the (Net) Present Value calculation.  In this case, you don't care (well, you do, just not for the purpose of comparison here) about the purchasing power of either option in the future, you just care how many dollars you would have.

Reality is probably that you are going to spend some and invest some.  I'll leave that to others and get back to the "invest it all" analysis now. ;)

i = annual investment return
n = number of years
P = annual payment for option 1
If i > 0,
FV of option 1 =          P * ((1+i)^n      - 1) / i
FV of option 2 = 1.16*P * (1+i)^(n-3) - 1) / i

If i = 0,
FV of option 1 =          P * n
FV of option 2 = 1.16*P * (n-3)

Solving for n when i=0 is straightforward and n=21.75 as noted a few times above.

Solving for n when i>0 is not so easy but one can use Excel's Goal Seek function to do so.  The time required for option 2 to catch option 1 is shown below.
0%  22 yrs
1%  24 yrs
2%  27 yrs
3%  32 yrs
4%  42 yrs
5%  89 yrs
...and for investment returns above 5.072%, option 1 is always better.

Why 5.072%?  Take the derivatives of the "i>0" equations with respect to n:
Option 1: ((i+1)^n*ln(i+1)*P)/i
Option 2: (1.16*(i+1)^(n-3)*ln(i+1)*P)/i

Divide #2 by #1 and get  1.16 / (1+i)^3.

We know option 1 starts at a higher value, so option 2 needs to increase faster than option 1 in order to catch it.  If it merely increases at the same rate, which happens when 1.16/(1+i)^3 = 1, option 1 is always better.  Solving this last equation gives i = (1.16)^(1/3) - 1 = 5.072%.

Of course, tidy math answers are one thing - correctly predicting future investment returns and spending/investing allocations are the real tests.  Good luck!

#### arebelspy

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##### Re: Arithmetic help gratefully accepted!
« Reply #12 on: December 24, 2015, 12:45:58 AM »
OOOhhhh MDM.  That post.

I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### Exflyboy

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##### Re: Arithmetic help gratefully accepted!
« Reply #13 on: January 30, 2016, 03:05:48 PM »
Hhahah..:)

I find myself is an eerily similar situation where I am 55 in October and can draw my pension on the day I turn 55.. Its not a huge amount.. roughly \$17k a year (its based back in the UK).

The implied growth rate if I leave it alone is 9%.. Great right?

Just two wrinkles.. 1) that GR is not guaranteed (its an estimate) and 2) the company i worked for has now split itself into two parts.. The sucessful part and the er.. shall we say "optimistic" part. Of course guess where they moved the pension obligations to?.. yup just like the airlines, the pensions now have to be funded from the part of the company that could well go TU!

Soooo.. the UK Government guarrantees pensions to 90% if you have NOT started taking bennies, but 100% if you have started receiving payouts... So there is a 10% reason to start taking the pension right there.

The problem is neither the Government nor the company guarantee the payout increases with inflation once the bennies have started to be taken.

I don't need the money, but I don't fancy losing any of it either. One option is to leave it in there one more year.. i.e till I'm 56. If the company fails then I potentially lose 10%, but hopefully the value of the payouts have grown by 9% as well.

Hmmmm.

#### arebelspy

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##### Re: Arithmetic help gratefully accepted!
« Reply #14 on: January 30, 2016, 03:22:01 PM »
I don't need the money, but I don't fancy losing any of it either. One option is to leave it in there one more year.. i.e till I'm 56. If the company fails then I potentially lose 10%, but hopefully the value of the payouts have grown by 9% as well.

Gain 9%/lose 10% is close to a coinflip.

Are the odds > 47% it fails within the next year?  Take the pension.  Otherwise, delay.

Unless the company is teetering on the brink of BK, delay seems to have a much higher EV than taking it at 55.
I am a former teacher who accumulated a bunch of real estate, retired at 29, spent some time traveling the world full time and am now settled with three kids.
If you want to know more about me, this Business Insider profile tells the story pretty well.
I (rarely) blog at AdventuringAlong.com. Check out the Now page to see what I'm up to currently.

#### Exflyboy

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##### Re: Arithmetic help gratefully accepted!
« Reply #15 on: January 30, 2016, 03:59:35 PM »
Yes if the GR is indeed accurate. I might hold off for a year and see if the company funds their portion of the pension fund.. The first year they cut back on their payment I might start withdrawing.

This is a bit like a mortgage as well, i,e if the real GR is nearer 4% rather then 9 then it may well pay to start withdrawing.. i.e earn more from the stash invested in stocks/bonds but llive off the pension.

#### MDM

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##### Re: Arithmetic help gratefully accepted!
« Reply #16 on: January 30, 2016, 04:06:28 PM »
I don't need the money, but I don't fancy losing any of it either. One option is to leave it in there one more year.. i.e till I'm 56. If the company fails then I potentially lose 10%, but hopefully the value of the payouts have grown by 9% as well.

Hmmmm.

+1 to what ARS said.

Also, if you don't take the pension, does that give you room for tax gain harvesting at 0% LTCG rate that would disappear with pension income?  Or similarly for taxation of traditional to Roth conversions: does the presence or absence of the pension change your marginal rate on those?

#### Exflyboy

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##### Re: Arithmetic help gratefully accepted!
« Reply #17 on: January 30, 2016, 04:48:20 PM »
Yes thats true, taking the pension does get taxed at normal income rates.

Of course if you want the max subsidy benefit for using the ACA, you are limited to to a MAGI of about \$24k... So the pension would cut into the amount I could convert to get a decent income.

Thats a good point.

Of course if we lived abroad then we could convert up to the 15% limit (\$75k?) because HC would not be a significant factor.